Open Problems

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Is there a faster algorithm for sorting signed permutations using reversals ?

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Given 3 signed permutations $\pi_1,\pi_2,\pi_3$, find an efficient algorithm that minimizes $\sum_{i=1}^3 d(\pi,\pi_i)$ (finding an exact solution is NP-hard [5]).

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Find the reversal distance between two signed digit sequences with equal number of occurrences of each digit.

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Find how many sequences of reversals realize d.

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Find among the minimum sequences one that has some additional properties.